HMM (Hidden Markov Model)-based cognitive radar confrontation dynamic modeling method

Abstract

The invention discloses a dynamic modeling method of a hidden Markov model, which comprises the following steps of: defining a radar-jammer master-slave confrontation mode, namely, when a radar is not interfered, setting an HMM-based information scheduling strategy matrix A and a transmitted pulse time-frequency parameter control strategy matrix B in coherent processing time according to a target detection task of the radar; a transmission pulse sequence is generated. An interference party extracts radar state parameters by using intercepted radar pulses, estimates a radar information scheduling strategy matrix A and a transmitting pulse time-frequency parameter control strategy matrix B, formulates an interference strategy matrix Aj and an interference signal time-frequency parameter control strategy matrix Bj, sends interference signals to the radar, and estimates Aj and Bj of the interference party after the radar receives the interference signals. And judging whether interference is valid or not, correspondingly adjusting the matrix A and the matrix B, and repeating the process to realize dynamic modeling of cognitive radar countermeasure.

Description

Technical Field

[0001] The present invention belongs to the technical field of electronic reconnaissance system modeling in the context of cognitive electronic warfare, and in particular relates to a cognitive radar confrontation dynamic modeling method based on Hidden Markov Models (HMM). Background Art

[0002] Hidden Markov models have broad application value in cognitive electronic warfare. Their core capability lies in modeling and reasoning in dynamic, uncertain environments. Existing cognitive radar countermeasures assume complete perception of the enemy's state information, formulating corresponding information scheduling methods and countermeasures in waveform design and optimization, power allocation, operating frequency band, confrontation time, and airspace, thereby establishing cognitive countermeasure models. However, actual confrontations are open-loop environments, where neither side can fully understand the other's state. For example, the jammer can only observe the radar transmitter state through its electronic support system and cannot directly perceive the radar's information scheduling and signal processing methods. Similarly, the radar cannot fully understand the jammer's jamming strategy. Therefore, how to appropriately assess the uncertainty brought about by incomplete information perception and thus establish dynamic models for cognitive radar countermeasures remains an unresolved scientific issue in the field of cognitive electronic warfare.

[0003] Cognitive electronic countermeasures originated from cognitive radio technology. "Cognition" refers to conscious intellectual activity involving thinking, reasoning, memorizing, imagining, learning, processing information, applying knowledge, and changing priorities. In the field of radar countermeasures, "cognitive radar" empowers radar systems with the ability to perceive their surroundings. Leveraging artificial intelligence (AI) technology, it continuously learns and infers the dynamics of the external environment, adaptively adjusting its operating mode. This includes adjusting transmit power, operating frequency, modulation, transmit waveform, and employing beam sidelobe blanking. This reduces the likelihood of radar interference and disruption in complex countermeasure environments. To achieve this, radars must understand the jammer's interference power, pattern, networking configuration, and location, and assess their electronic reconnaissance capabilities. A radar's core anti-interference capability lies primarily in its ability to identify jammers' jamming signals and strategies. This requires a large number of manually annotated jammer signal samples encompassing all jamming patterns and strategies, a practical impossibility. Similarly, it's impossible for the jammer to fully understand the radar's anti-jamming measures and signal processing methods, especially to identify the radar's information scheduling strategy. In actual combat, electronic support systems can only provide partial information about the radar transmitter's operating status, and the effectiveness of their jamming doesn't fully depend on radar information. For example, traditional suppression coefficients don't account for the radar's anti-jamming improvement factor and therefore only represent the signal-to-interference ratio (SJR) at the radar antenna aperture. Under conditions of incomplete information, existing AI-based countermeasure models and effectiveness evaluation methods are inadequate for realistic combat environments, making true cognitive countermeasures impossible. Therefore, dynamic modeling of cognitive radar countermeasures is a key issue urgently needed in cognitive electromagnetic spectrum warfare. Summary of the Invention

[0004] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide an HMM-based cognitive radar countermeasure dynamic modeling method to solve the problems of difficulty in describing the radar information scheduling strategy after the jammer intercepts the radar transmitted pulse sequence and what countermeasures the radar takes after receiving the jamming signal in the cognitive radar countermeasure modeling, thereby realizing cognitive electronic countermeasures under incomplete information conditions.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A cognitive radar countermeasure dynamic modeling method based on HMM includes the following steps:

[0007] Step 1: Construct the master-slave confrontation scenario between the radar and the jammer, set the confrontation round iter, formulate the information scheduling strategy matrix A and the time-frequency parameter control strategy matrix B of the transmitted pulse within the coherent processing time based on the target detection task under the condition that the radar is not jammed, and generate the transmitted pulse sequence S r =[s1, s2,..., s N , where s N represents the Nth radar pulse, and N represents the number of transmitted radar pulses;

[0008] Step 2: The jammer estimates the matrices A and B based on the intercepted radar transmitted pulse sequence S r ′ = [s1, s2,..., s M , formulates the interference strategy matrix A j and the time-frequency parameter control strategy matrix B j of the interference signal according to the interference strategy, and jams the radar with the interference signal S j =[s 1j , s 2j ,... s Nj , where M represents the number of intercepted pulses, M ≤ N, and s Nj represents the Nth interference signal;

[0009] Step 3: The radar receives the interference signal S j , estimates the matrices A j and B j , calculates the adjusted Rand index (ARI) of {S j , S r}, and judges the interference effect of S j : If the adjusted Rand index is greater than 0, the interference is effective, and the radar adjusts the matrices A and B to generate a new transmitted pulse sequence;

[0010] Step 4: If the confrontation round < iter, return to Step 2, otherwise, output the confrontation result.

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0012] 1. According to various uncertain factors faced by the cognitive radar confrontation dynamic modeling, the present invention regards the state characteristic quantity of the radar transmitter as a Markov process hidden in the transmitted pulse sequence, and establishes a cognitive radar confrontation dynamic model based on HMM, that is, according to the signal processing and information scheduling methods possessed by the radar, constructs the information scheduling strategy matrix A of the radar and the time-frequency parameter control strategy matrix B of the transmitted pulse within the coherent processing time, and thus generates the radar transmitted pulse sequence S r , providing a theoretical support for identifying the radar working mode.

[0013] 2. This invention uses the signal processing method of the jammer's electronic support system to take the intercepted radar pulses as training samples for the unsupervised learning algorithm, and uses the Baum-Welch algorithm to identify the radar working state. On this basis, the jamming strategy matrix A is formulated. j and interference signal time-frequency parameter control strategy matrix B j , sends a jamming signal S to the radar j , which can effectively simulate the interference process of radar.

[0014] 3. According to the anti-interference strategy after the radar is interfered with, the present invention uses HMM to estimate the interference strategy matrix A of the interference signal j and interference signal time-frequency parameter control strategy matrix B j , calculate {S j ,S r The Adjusted Rand Index (ARI) of the radar is used to determine whether the jamming is effective, and whether the ARI is greater than 0 is used as the basis for judging whether the jamming is effective, thereby realistically simulating the radar's anti-jamming process. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Schematic diagram of cognitive electronic warfare operations.

[0016] Figure 2 is the time-frequency diagram of the transmitted pulse train.

[0017] Figure 3 It is a binary image of the time-frequency diagram of the intercepted radar signal.

[0018] Figure 4 is the peak distribution of the binary image after Hough transform.

[0019] Figure 5 This is a modeling and simulation flow chart of the present invention.

[0020] Figure 6 The Rand Index ARI change chart is adjusted for the Rand Index RI during cognitive radar confrontation.

[0021] Figure 7 This is a graph showing the change in radar state estimation error for the jammer during cognitive radar confrontation. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0023] From the perspective of system confrontation, cognitive electronic warfare operations are mainly composed of the processes of "cognitive interception - cognitive processing - cognitive decision-making - cognitive interference", forming a closed loop from reconnaissance to interference to evaluation, as shown in the attached figure. Figure 1 Obviously, there is incomplete information in the cognitive interception stage, which leads to non-negligible cognitive bias and uncertainty in the cognitive processing stage, which in turn causes cognitive decision-making errors and the inability to implement effective cognitive interference.

[0024] Taking cognitive radar confrontation as an example, the proposed confrontation simulation model is as follows:

[0025]

[0026] Formula (1) is the radar state equation, x = [A m ,f c ,B w ,M d ,prf] is the radar characteristic parameter, that is, the radar state variable, where A m represents the pulse amplitude, f c Indicates the pulse carrier frequency, B w Indicates the pulse bandwidth, M d Indicates the intra-pulse modulation mode, prf indicates the pulse repetition frequency; μ a Represents the radar anti-interference measures. Among them, the interference party can measure the radar state x through the perception system, and μ a It is an unmeasurable system variable and can be regarded as the "hidden variable" of the radar.

[0027] Formula (2) is the perception result of the interference party's cognitive system on the radar working state, which includes the radar anti-interference measures μ a The estimate of x is incomplete information, z includes the estimated error of the radar state x. When the confrontation scenario is determined, the signal detection and estimation method can be used to obtain the estimated value of x. It is an estimated value obtained through prior knowledge and radar working status.

[0028] Formula (3) is the estimation of the current working state of the radar by the interference party's cognitive system, which has a large uncertainty. Formula (4) is the interference pattern made based on the estimation result of Formula (3). Due to the incompleteness of the estimation of the radar anti-interference measures, after y acts on the radar, it is necessary to observe whether the radar state changes through Formula (2) and then correct the μ a The entire confrontation process can be implemented using the "dynamic modeling method based on hidden Markov model":

[0029] First, the working process of the detection receiver of the electronic reconnaissance system is briefly described. d ) in the monitoring frequency band, the receiver receives mixed signals including target radar signals and other interference signals, and obtains N target radar transmission pulses after signal sorting; the receiver will measure the pulse amplitude A m , center frequency f c , instantaneous bandwidth B w , intra-pulse modulation mode M d Due to factors such as signal sorting errors and random channel fading, these measurements appear as random sequences of length N that follow a certain probability distribution. The mean and variance (μ, σ) of the measurement sequence are the basis for determining its true value and random error. A common practice is to determine a threshold based on σ. When the measured value is below the threshold, the change is considered insignificant; when it exceeds the threshold, the change is considered significant.

[0030] When the radar is not interfered with, the radar will set the transmission pulse state x=[A m ,f c ,B w ,M d ,prf] and remain unchanged during its coherent processing time; when the radar is subjected to suppression interference, it randomly changes one or more parameters in x according to its anti-interference strategy, such as changing the center frequency f according to a certain rule c When the radar is subjected to deception interference, the transmit pulse amplitude A is changed according to the information scheduling rules based on the identification of the deception interference type. m , center frequency f c , instantaneous bandwidth B w , intra-pulse modulation mode M d and pulse repetition frequency prf, generating a new transmit pulse sequence S r =[s1,s2,…,s N ] to avoid the interference released by the jammer. The jammer must re-intercept the radar's transmitted pulses, analyze its status, adjust the jamming strategy, and continue the game with the radar.

[0031] In the observation period (0~t d) The radar pulse received by the interference party's detection receiver is expressed as is the radar pulse quantization length, is the number of radar pulses intercepted. Since the receiver is measuring the radar transmitter state x=[A m ,f c ,B w ,M d ,prf], each measured quantity is measured independently, for example, the pulse amplitude A m Usually the maximum value of each intercepted pulse amplitude is taken. The pulse maxima constitute a random sequence with relatively fixed mean and variance; for the center frequency f c , instantaneous bandwidth B w The measurement of pulse repetition frequency (PRF) is usually obtained by performing time-frequency joint analysis on each intercepted pulse, as shown in the attached figure. Figure 2 The following is a pseudo-Wigner-Ville transform time-frequency diagram of the four intercepted radar pulses. The main parameters of the radar transmitter are as follows:

[0032] Pulse power P t =100W; Transmit pulse width T = 3μs; Intra-pulse modulation mode: LFM, FM bandwidth B = 30MHz; Center frequency f c =1.8GHz; pulse repetition period PRI = 15μs.

[0033] As attached Figure 3 The following is a binary image of the intercepted radar signal time-frequency diagram. The bandwidth B of the radar signal can be estimated by detecting the length of the three oblique lines along the frequency axis. w , the repetition period PRI of the radar pulse can be estimated by measuring the interval of the slash line along the time axis (prf = 1 / PRI), the frequency modulation slope k of the LFM signal can be estimated by measuring the slope of the slash line, and the time difference between the starting point and the end point of the slash line is the pulse width T, etc. To estimate the carrier frequency f of the radar pulse c , through Hough transform Figure 3 The oblique lines in the figure are transformed into points on the time-frequency plane, as shown in the following figure. Figure 4 , detect the peak position to get the carrier frequency f c estimated value.

[0034] When the jammer obtains the radar transmit pulse state parameters, according to its jamming strategy S j ={′WBJ′,′NBJ′,′C&I′,′DenseTargets′,′R&VDecept′}, where the five terms represent broadband noise suppression, narrowband smart noise suppression, slice jamming, dense false target jamming, and range-speed deception jamming, respectively. The jamming strategy matrix A is formulated. j and interference signal time-frequency parameter control strategy matrix Bj , sends a jamming signal S to the radar j =[s 1j ,s 2j ,...s Nj ].

[0035] When the radar receives the changed interference signal S released by the jammer j After that, we will analyze its interference strategy matrix A j and interference signal time-frequency parameter control strategy matrix B j , compared with the new transmit pulse sequence S r With the interference signal S j When the interference is judged to be effective, the state characteristic transfer matrix A and the transmission pulse time-frequency parameter control strategy matrix B within the coherent processing time are adjusted to generate a new transmission pulse sequence S r .

[0036] In summary, reference Figure 5 As shown, the method proposed by the present invention consists of the following steps:

[0037] Step 1: Construct a radar-jammer master-slave confrontation scenario, set the confrontation round iter, and formulate the information scheduling strategy matrix A based on the Hidden Markov Model (HMM) and the transmission pulse time-frequency parameter control strategy matrix B within the coherent processing time according to the target detection task under the radar undisturbed condition, and generate the transmission pulse sequence S r =[s1,s2,…,s N ], where s N Indicates the Nth radar pulse, where N is the number of radar pulses transmitted.

[0038] Step 2: The jammer transmits a pulse sequence S′ based on the intercepted radar signal. r =[s1,s2,…,s M ], M≤N, use the Baum-Welch algorithm and other methods to estimate the radar information scheduling strategy matrix A and the pulse transmission time-frequency parameter control strategy matrix B within the coherent processing time, according to the interference strategy S j ={′WBJ′,′NBJ′,′C&I′,′DenseTargets′,′R&VDecept′}, where the five terms represent broadband noise suppression, narrowband smart noise suppression, slice jamming, dense false target jamming, and range-speed deception jamming, respectively. The jamming strategy matrix A is formulated. j and interference signal time-frequency parameter control strategy matrix B j , sends a jamming signal S to the radar j =[s 1j ,s 2j ,…sNj , where M represents the number of intercepted pulses, s Nj represents the Nth interference signal.

[0039] Step 3: The radar receives the interference signal S j , estimate the interference strategy matrix A of the interference signal j and the time-frequency parameter control strategy matrix B of the interference signal j , calculate the Adjusted Rand Index (ARI) of {S j , S r}, and judge the interference effect of S j : If ARI > 0, the interference is effective, and the radar adjusts the information scheduling strategy matrix A and the time-frequency parameter control strategy matrix B of the transmitted pulses within the coherent processing time to generate a new transmitted pulse sequence.

[0040] Step 4: If the number of confrontation rounds < iter, return to Step 2; otherwise, output the confrontation result.

[0041] In Step 1, the method for formulating the information scheduling strategy matrix A based on the Hidden Markov Model (HMM) and the time-frequency parameter control strategy matrix B of the transmitted pulses within the coherent processing time is as follows:

[0042] Step 11, set the characteristic parameters x of N radar pulses S r as x = [A m , f c , B w , M d , prf], where A m represents the pulse amplitude, f c represents the pulse carrier frequency, B w represents the pulse bandwidth, M d represents the in-pulse modulation mode, and prf represents the pulse repetition frequency. The radar changes these characteristic parameters according to its information scheduling strategy.

[0043] Step 12, define the Hidden Markov Model (HMM) of the radar as consisting of the following five-tuple:

[0044] λ = (S r , O, A, B, π)

[0045] Where: The state set is the transmitted pulse sequence S r , the observation set is represented as O = {o1, o2,..., o M}, o M is the Mth observation value, M is the number of possible observation values, and the information scheduling strategy matrix A is used as the state transition matrix, represented as A = [aij ] N×N , a ij Indicates that from state s i Transfer to s j The probability of The control strategy matrix B of the time-frequency parameters of the transmitted pulses within the coherent processing time is used as the observation probability matrix, which is expressed as B = [b j (k)] N×M , b j (k) means in state s j Generate observation o k The probability of (such as emission probability), The initial state distribution π is expressed as π=[π i ],π i Indicates that the initial state is s i Probability

[0046] Step 13: Based on the radar pulse characteristic parameter x obtained in step 11 and the target detection task under radar undisturbed conditions, construct the information scheduling strategy matrix A and the transmission pulse time-frequency parameter control strategy matrix B within the coherent processing time.

[0047] Step 14, generate the transmit pulse sequence S r =[s1,s2,...,s N ].

[0048] In Step 2, the Baum-Welch algorithm is used to estimate the radar's information scheduling strategy matrix A and the transmission pulse time-frequency parameter control strategy matrix B within the coherent processing time, as follows:

[0049] Step 21, construct the objective function.

[0050] The jammer transmits a pulse sequence S from the intercepted radar r 'Extract observation sequence O = {o1, o2, ..., o M The goal of the Baum-Welch algorithm is to maximize the likelihood function of the observation sequence O:

[0051]

[0052] Where, Q=(q1,q2,…,q M ) is the hidden state sequence, q M is the Mth hidden state in Q, and P(O,Q|λ) is the joint probability of (O,Q) given the known radar adversarial model λ.

[0053] Step 22, E: Calculate the expectation.

[0054] The forward-backward algorithm is used to calculate the following key probabilities:

[0055] (1) Forward probability a t (i), i=1,2,…N

[0056] a t (i)=P(o1,o2…,o M ,q t =s i |λ),t=1,2,…M Recursive formula:

[0057]

[0058] (2) Backward probability β t (i), i=1,2,…N

[0059] β t (i) = P(o t+1 ,o t+2 ,…,o M |q t =s i ,λ),t=1,2,…M Recursive formula:

[0060]

[0061] (3) State transition probability ξ t (i,j),i=1,2,…N,j=1,2,…N

[0062] ξ t (i,j)=P(q t =s i ,q t+1 =s j |O,λ),t=1,2,…M

[0063] Calculation formula:

[0064]

[0065] The denominator

[0066] (4) State residence probability γ t (i)

[0067]

[0068] Step 23, M step: parameter update.

[0069] Using the expected value calculated in step E, update the model parameters, including:

[0070] (1) Update the initial state distribution π

[0071] π i =γ1(i), i=1,2,…N

[0072] (2) Update the information scheduling strategy matrix A

[0073]

[0074] (3) Update the transmit pulse time-frequency parameter control strategy matrix B

[0075]

[0076] Among them, v k is the observed value o t The corresponding index, γ1(i) is the initial value of the state residence probability.

[0077] Step 24, convergence judgment.

[0078] Calculate the log-likelihood logP(O|λ). If the change is less than the set value ∈, stop the iteration, where 0<∈<1.

[0079] In Step 3, the radar receives the interference signal S j , estimate the interference strategy matrix A of the interference signal j and interference signal time-frequency parameter control strategy matrix B j , calculate {S j ,S r The Adjusted Rand Index (ARI) is calculated as follows:

[0080] Step 31: Set and It is right j ,S r} two clustering results, n is the total number of samples, Indicates that in S j and S r The sample pairs that are classified into the same category in Indicates that in S j and S r The sample pairs are classified into different classes. is the number of all sample pairs.

[0081] Step 32: Calculate the Rand Index (RI):

[0082]

[0083] Step 33: Calculate the expected value of the Rand Index RI:

[0084]

[0085] Among them, r and s are the number of categories of the two clustering results, n ij Belong to the cluster and clustering The number of samples, n i Belongs to cluster The number of samples in n j Belongs to cluster The number of samples in .

[0086] Step 34: Calculate the Adjusted Rand Index (ARI)

[0087]

[0088] The ARI value range is between [-1, 1], where 1 means that the two clustering results are exactly the same, 0 means that the two clustering results are equivalent to random division, and -1 means that the two clustering results are completely opposite.

[0089] Step 35: If ARI>0, the interference is effective, and the radar adjusts the information scheduling strategy matrix A and the transmission pulse time-frequency parameter control strategy matrix B within the coherent processing time to generate a new transmission pulse sequence S r =[s1,s2,...,s N ], otherwise, keep the matrices A and B unchanged. The adjustment method may be, for example, changing the probability value or probability distribution function of each row of matrices A and B.

[0090] In order to verify the effectiveness of the proposed method, the present invention selects the radar working state characteristic parameter x = [A m ,f c ,B w ,M d ,prf] in the center frequency f c ={f1,f2,f3,f4,f5} is the object to realize the frequency hopping anti-interference strategy of radar.

[0091] Assume that the radar information scheduling strategy matrix A is:

[0092] A=[0.5 0.3 0.1 0.05 0.05; 0.2 0.5 0.1 0.1 0.1; 0.1 0.1 0.5 0.2 0.1; 0.10.1 0.2 0.5 0.1; 0.1 0.1 0.1 0.2 0.5]

[0093] Each row of A corresponds to a frequency hopping strategy, that is, the center frequency f cJump among {f1,f2,f3,f4,f5} with corresponding probability.

[0094] The transmit pulse time-frequency parameter control strategy matrix B is:

[0095] B=[1 / 6 1 / 6 1 / 6 1 / 6 1 / 6 1 / 6; 1 / 5 1 / 5 1 / 5 1 / 5 1 / 10 1 / 10; 0 1 / 2 0 1 / 4 1 / 40; 1 / 2 1 / 5 1 / 5 0 1 / 10 0; 1 / 10 1 / 10 1 / 10 1 / 10 1 / 10 1 / 2]

[0096] The number of columns in B corresponds to the frequency hopping strategy of the transmitted pulse within the radar coherent processing time, and each row of B is a different frequency hopping transition probability.

[0097] The radar generates a frequency hopping transmit pulse sequence S using matrices A and B. r =[s1,s2,…,s N ], where N=1000.

[0098] Assume that the jammer intercepts the radar pulse S r ′=[s1,s2,…s M ], M = 100, and through Step 21 to Step 24, the estimated values ​​of the radar information scheduling strategy matrix A and the transmission pulse time-frequency parameter control strategy matrix B within the coherent processing time are obtained:

[0099]

[0100] The interference party follows the matrix and According to the interference strategy S j ={'WBJ','NBJ','C&I','DenseTargets','R&VDecept'}, where they represent broadband noise suppression, narrowband smart noise suppression, slice jamming, dense false target jamming, and range-velocity deception jamming, respectively. The jamming strategy matrix A is formulated. j and interference signal time-frequency parameter control strategy matrix B j , sends a jamming signal S to the radar j =[s 1j ,s 2j ,…s Nj ].

[0101] The radar receives the interference signal S j After that, calculate {S j ,S rIf ARI>0, the interference is effective, and the radar adjusts the information scheduling strategy matrix A and the transmission pulse time-frequency parameter control strategy matrix B within the coherent processing time to generate a new transmission pulse sequence S r =[s1,s2,...,s N ], otherwise, keep matrices A and B unchanged.

[0102] As attached Figure 6 The figure shows the simulation results of the confrontation with iter=30 rounds, and the curves of RI and ARI are shown. As can be seen from the figure above, every time the radar changes its information scheduling strategy matrix A and the control strategy matrix B of the time-frequency parameters of the pulses transmitted during the coherent processing time, the jammer will fail in multiple confrontation rounds. The main reason is that the number of intercepted pulses used by the jammer when estimating the radar's information scheduling strategy matrix A and the control strategy matrix B of the time-frequency parameters of the pulses transmitted during the coherent processing time is much smaller than the number of pulses transmitted by the radar, and the radar analyzes the jammer's interference strategy matrix A. j and interference signal time-frequency parameter control strategy matrix B j All interference pulse sequences are used, Figure 7 This is the curve of the radar's state estimation error for the jammer during cognitive radar confrontation. It can be seen from the figure that the radar accurately estimates the jammer's jamming strategy.

[0103] In summary, dynamic modeling in cognitive radar confrontation faces many problems. Radar confrontation is a dynamic game process between the enemy and us, and both sides will constantly adjust their strategies according to the actions of the other side. In dynamic modeling, it is necessary to consider the strategy changes of both sides and their mutual influence at the same time. It is very complicated to establish a model that can accurately describe this dynamic game process. In order to solve this problem, the present invention proposes a dynamic modeling method of cognitive radar confrontation based on HMM: define the radar-jammer as a master-slave confrontation mode, that is, when the radar is not interfered with, set the HMM-based information scheduling strategy matrix A and the transmission pulse time-frequency parameter control strategy matrix B within the coherent processing time according to its target detection task to generate a transmission pulse sequence. The jammer uses the intercepted radar pulse to extract the radar state parameters and estimate the radar information scheduling strategy matrix A and the transmission pulse time-frequency parameter control strategy matrix B, and formulates the interference strategy matrix A j and interference signal time-frequency parameter control strategy matrix B j , sends a jamming signal to the radar. After receiving the jamming signal, the radar estimates the jammer’s A j and B j Determine whether the jamming is effective and adjust matrices A and B accordingly. Repeating this process can achieve dynamic modeling of cognitive radar countermeasures.

Claims

1. A cognitive radar confrontation dynamic modeling method based on HMM, characterized by: It includes the following steps: Step 1: Construct a radar-jammer master-slave confrontation scenario, set the confrontation round iter, and formulate the information scheduling strategy matrix A based on the hidden Markov model and the transmission pulse time-frequency parameter control strategy matrix B within the coherent processing time according to the target detection task under the radar undisturbed condition, and generate the transmission pulse sequence S r =[s1,s2,...,s N ], where s N represents the Nth radar pulse, where N represents the number of radar pulses transmitted; Step 2: The jammer transmits a pulse sequence S based on the intercepted radar signal. r '=[s1,s2,…,s M ] Estimate matrices A and B, and formulate interference strategy matrix A based on the interference strategy j and interference signal time-frequency parameter control strategy matrix B j , sends a jamming signal S to the radar j =[s 1j ,s 2j ,...s Nj ], where M represents the number of pulses intercepted, M≤N, s Nj represents the Nth interference signal; Step 3: The radar receives the interference signal S j , estimate the matrix A j and B j , calculate {S j ,S r }Adjusted Rand Index (ARI), judging S j Interference effect: If the adjusted Rand index is greater than 0, the interference is effective, and the radar adjusts matrices A and B to generate a new transmit pulse sequence; Step 4, if the adversarial round < iter, return to Step 2, otherwise, output the adversarial result.

2. The HMM-based cognitive radar countermeasure dynamic modeling method according to claim 1, characterized in that: The method for formulating the information scheduling strategy matrix A based on the hidden Markov model and the time-frequency parameter control strategy matrix B of the transmitted pulse within the coherent processing time in Step 1 is as follows: Step 11, set the characteristic parameter x of N transmitted radar pulses, and the radar changes the characteristic parameter according to its information scheduling strategy; Step 12, define that the hidden Markov model of the radar consists of the following five-tuple: λ=(S r ,O,A,B,π) Where: Transmit pulse sequence S r As a state set, the observation set is represented as O = {o1, o2, ..., o M }, o M is the Mth observation value, and the initial state distribution π is expressed as π=[π i ],π i Indicates that the initial state is s i of Probability; Step 13, based on the characteristic parameter x and combined with the target detection task under the condition that the radar is not interfered, construct the information scheduling strategy matrix A and the time-frequency parameter control strategy matrix B of the transmitted pulse within the coherent processing time; Step 14: Generate a transmit pulse sequence S r =[s1,s2,...,s N ].

3. The HMM-based cognitive radar countermeasure dynamic modeling method according to claim 2, characterized in that: The characteristic parameter x=[A m ,f c ,B w ,M d ,prf], where A m represents the pulse amplitude, f c Indicates the pulse carrier frequency, B w Indicates the pulse bandwidth, M d Indicates the intra-pulse modulation mode, and prf indicates the pulse repetition frequency.

4. The HMM-based cognitive radar countermeasure dynamic modeling method according to claim 2, characterized in that: In the five-tuple, the information scheduling strategy matrix A is used as the state feature transfer matrix, which is expressed as A=[a ij ] N×N , a ij Indicates that from state s i Transfer to s j The probability of a ij =P(s t+1 =s j |s t =s j ), The control strategy matrix B of the time-frequency parameters of the transmitted pulses within the coherent processing time is used as the observation probability matrix, which is expressed as B = [b j (k)] N×M , b j (k) means in state s j Generate observation o k The probability of b j (k)=P(o t =o k |s t =s j ), Initially in state s i The probability π i =P(s1=s i ), 5. The HMM-based cognitive radar countermeasure dynamic modeling method according to claim 2, characterized in that: In Step 2, use the Baum-Welch algorithm to estimate matrices A and B as follows: Step 21: The jammer transmits a pulse sequence S from the intercepted radar. r 'Extract observation sequence O={o1,o2,...,o M The goal of the Baum-Welch algorithm is to maximize the likelihood function of the observation sequence O: Where, Q=(q1,q2,...,q M ) is the hidden state sequence, q M is the Mth hidden state in the observation sequence O, P(O,Q|λ) is the (O,Q) joint probability of the known radar adversarial model λ; Step 22, calculate the forward probability a using the forward-backward algorithm t (i) Backward probability β t (i) State transition probability ξ t (i, j) and state residence probability γ t (i); Step 23, update the model parameters using the calculation result of Step 22, including: (1) Update the initial state distribution π, π i =γ1(i); (2) Update the state feature transfer matrix, that is, matrix A, (3) Update the observation probability matrix, that is, matrix B, Among them, v k is the observed value o t The corresponding indexes are i=1,2,…N, j=1,2,…N, t=1,2,…M, k=1,2,…M, and γ1(i) is the initial value of the state residence probability. Step 24, calculate the log-likelihood logP(O∣λ), if the change amount is less than ∈, stop the iteration, where 0 < ∈ < 1.

6. The HMM-based cognitive radar countermeasure dynamic modeling method according to claim 5, characterized in that: In step 22, the forward probability a t (i)=P(o1,o2…,o M ,q t =s i |λ), the recursive formula is as follows: Backward probability β t (i) = P(o t+1 ,o t+2 ,…,o M |q t =s i ,λ), the recursive formula is as follows: State transition probability ξ t (i,j)=P(q t =s i ,q t+1 =s j |O,λ), the calculation formula is as follows: in, 7. The HMM-based cognitive radar countermeasure dynamic modeling method according to claim 1, 5 or 6, characterized in that: The interference strategies include wideband noise suppression, narrowband smart noise suppression, slice interference, dense false target interference, and range-velocity deception interference.

8. The HMM-based cognitive radar countermeasure dynamic modeling method according to claim 1, characterized in that: In step 3, the radar receives the interference signal S j , estimate the matrix A j and B j , calculate {S j ,S r The steps for adjusting the Rand Index are as follows: Step 31, set and It is right j ,S r } two clustering results, n is the total number of samples, Indicates that in S j and S r The sample pairs that are classified into the same category in Indicates that in S j and S r The sample pairs are classified into different classes. is the number of all sample pairs; Step 32, calculate the Rand index: Step 33, calculate the expected value of the Rand index: Among them, r and s are the number of categories of the two clustering results, n ij Belong to the cluster and clustering The number of samples, n i Belongs to cluster The number of samples, n j Belongs to cluster The number of samples; Step 34, calculate the adjusted Rand index: The ARI value ranges between [-1, 1]. 1 indicates that the two clustering results are exactly the same, 0 indicates that the two clustering results are equivalent to a random partition, and -1 indicates that the two clustering results are exactly opposite; Step 35: If ARI>0, the jamming is effective, and the radar adjusts A and B to generate a new transmit pulse sequence S. r =[s1,s2,...,s N ], otherwise, keep matrices A and B unchanged.

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